Resolution beyond the diffraction limit for regularized object restoration

We propose a new formulation of Miller's regularization theory, which is particularly suitable for object restoration problems. By means of simple geometrical arguments, we obtain upper and lower bounds for the errors on regularized solutions. This leads to distinguish between ' Holder continuity ' which is quite good for practical computations and ` logarithmic continuity ' which is very poor. However, in the latter case, one can reconstruct local weighted averages of the solution. This procedure allows for precise valuations of the resolution attainable in a given problem. Numerical computations, made for object restoration beyond the diffraction limit in Fourier optics, show that, when logarithmic continuity holds, the resolution is practically independent of the data noise level. © 1980 Taylor & Francis Group, LLC.

Spectrally efficient cooperative diversity protocol for uplink wireless transmission

A spectrally efficient cooperative protocol for uplink wireless transmission in a centralised communication system is proposed, where each of the N users play the relaying and source roles simultaneously by using superposition (SP) modulation. The probability density function of the mutual information between SP-modulated transmitted and received signals of the cooperative uplink channels is derived. Using the high-signal-to-noise ratio (SNR) approximation of this density function, the outage probability formula of the system as well as its easily computable tight upper and lower bounds are obtained and these formulas are evaluated numerically. Numerical results show that the proposed strategy can achieve around 3 dB performance gain over comparable schemes. Furthermore, the multiplexing and diversity tradeoff formula is derived to illustrate the optimal performance of the proposed protocol, which also confirms that the SP relaying transmission does not cause any loss of data rate. Moreover, performance characterisation in terms of ergodic and outage capacities are studied and numerical results show that the proposed scheme can achieve significantly larger outage capacity than direct transmission, which is similar to other cooperative schemes. The superiority of the proposed strategy is demonstrated by the fact that it can maintain almost the same ergodic capacity as the direct transmission, whereas the ergodic capacity of other cooperative schemes would be much worse.

Variance-Constrained Capacity of the Molecular Timing Channel with Synchronization Error

Molecular communication is set to play an important role in the design of complex biological and chemical systems. An important class of molecular communication systems is based on the timing channel, where information is encoded in the delay of the transmitted molecule - a synchronous approach. At present, a widely used modeling assumption is the perfect synchronization between the transmitter and the receiver. Unfortunately, this assumption is unlikely to hold in most practical molecular systems. To remedy this, we introduce a clock into the model - leading to the molecular timing channel with synchronization error. To quantify the behavior of this new system, we derive upper and lower bounds on the variance-constrained capacity, which we view as the step between the mean-delay and the peak-delay constrained capacity. By numerically evaluating our bounds, we obtain a key practical insight: the drift velocity of the clock links does not need to be significantly larger than the drift velocity of the information link, in order to achieve the variance-constrained capacity with perfect synchronization.

Statistical Eigenmode Transmission for the MU-MIMO Downlink in Rician Fading

In this paper, we study the achievable ergodic sum-rate of multiuser multiple-input multiple-output downlink systems in Rician fading channels. We first derive a lower bound on the average signal-to-leakage-and-noise ratio by using the Mullen’s inequality, and then use it to analyze the effect of channel mean information on the achievable ergodic sum-rate. A novel statistical-eigenmode space-division multiple-access (SESDMA) downlink transmission scheme is then proposed. For this scheme, we derive an exact analytical closed-form expression for the achievable ergodic rate and present tractable tight upper and lower bounds. Based on our analysis, we gain valuable insights into the system parameters, such as the number of transmit antennas, the signal-to-noise ratio (SNR) and Rician K-factor on the system sum-rate. Results show that the sum-rate converges to a saturation value in the high SNR regime and tends to a lower limit for the low Rician K-factor case. In addition, we compare the achievable ergodic sum-rate between SE-SDMA and zeroforcing beamforming with perfect channel state information at the base station. Our results reveal that the rate gap tends to zero in the high Rician K-factor regime. Finally, numerical results are presented to validate our analysis.

I/Q imbalance in AF dual-hop relaying: Performance analysis in Nakagami-m fading

We analyze the performance of amplify-and-forward dual-hop relaying systems in the presence of in-phase and quadrature-phase imbalance (IQI) at the relay node. In particular, an exact analytical expression for and tight lower bounds on the outage probability are derived over independent, non-identically distributed Nakagami-m fading channels. Moreover, tractable upper and lower bounds on the ergodic capacity are presented at arbitrary signal-to-noise ratios (SNRs). Some special cases of practical interest (e.g., Rayleigh and Nakagami-0.5 fading) are also studied. An asymptotic analysis is performed in the high SNR regime, where we observe that IQI results in a ceiling effect on the signal-to-interference-plus-noise ratio (SINR), which depends only on the level of I/Q impairments, i.e., the joint image rejection ratio. Finally, the optimal I/Q amplitude and phase mismatch parameters are provided for maximizing the SINR ceiling, thus improving the system performance. An interesting observation is that, under a fixed total phase mismatch constraint, it is optimal to have the same level of transmitter (TX) and receiver (RX) phase mismatch at the relay node, while the optimal values for the TX and RX amplitude mismatch should be inversely proportional to each other.

O problema da árvore de suporte de custo mínimo com restrições de peso

Nesta tese abordam-se várias formulações e diferentes métodos para resolver o Problema da Árvore de Suporte de Custo Mínimo com Restrições de Peso (WMST – Weight-constrained Minimum Spanning Tree Problem). Este problema, com aplicações no desenho de redes de comunicações e telecomunicações, é um problema de Otimização Combinatória NP-difícil. O Problema WMST consiste em determinar, numa rede com custos e pesos associados às arestas, uma árvore de suporte de custo mínimo de tal forma que o seu peso total não exceda um dado limite especificado. Apresentam-se e comparam-se várias formulações para o problema. Uma delas é usada para desenvolver um procedimento com introdução de cortes baseado em separação e que se tornou bastante útil na obtenção de soluções para o problema. Tendo como propósito fortalecer as formulações apresentadas, introduzem-se novas classes de desigualdades válidas que foram adaptadas das conhecidas desigualdades de cobertura, desigualdades de cobertura estendida e desigualdades de cobertura levantada. As novas desigualdades incorporam a informação de dois conjuntos de soluções: o conjunto das árvores de suporte e o conjunto saco-mochila. Apresentam-se diversos algoritmos heurísticos de separação que nos permitem usar as desigualdades válidas propostas de forma eficiente. Com base na decomposição Lagrangeana, apresentam-se e comparam-se algoritmos simples, mas eficientes, que podem ser usados para calcular limites inferiores e superiores para o valor ótimo do WMST. Entre eles encontram-se dois novos algoritmos: um baseado na convexidade da função Lagrangeana e outro que faz uso da inclusão de desigualdades válidas. Com o objetivo de obter soluções aproximadas para o Problema WMST usam-se métodos heurísticos para encontrar uma solução inteira admissível. Os métodos heurísticos apresentados são baseados nas estratégias Feasibility Pump e Local Branching. Apresentam-se resultados computacionais usando todos os métodos apresentados. Os resultados mostram que os diferentes métodos apresentados são bastante eficientes para encontrar soluções para o Problema WMST.

A Comparative Study of a Low Doppler Shift in a Carrier Tracking Loop for GPS

This paper compares a carrier tracking scenario when a received Global Positioning System (GPS) signal has low Doppler frequency. It is shown that if the Numerically Controlled Oscillator (NCO) is quantized to 1 bit, the carrier tracking loop is unable to keep track of the incoming signal which leaves the tracking loop oscillating between the upper and lower bounds of the tracking loop bandwidth. One way of overcoming this problem is presented and compared with another existing solution, found in the literature, providing comparative results from the use of real-recorded off the air GPS L1 signals. Results show that the proposed method performs better tracking performance compared with the existing solution which it requires much less hardware complexity.

On the numerical computation of the Mittag-Leffler function

Recently simple limiting functions establishing upper and lower bounds on the Mittag-Leffler function were found. This paper follows those expressions to design an efficient algorithm for the approximate calculation of expressions usual in fractional-order control systems. The numerical experiments demonstrate the superior efficiency of the proposed method.

On the numerical computation of the Mittag-Leffler function

Recently simple limiting functions establishing upper and lower bounds on the Mittag-Leffler function were found. This paper follows those expressions to design an efficient algorithm for the approximate calculation of expressions usual in fractional-order control systems. The numerical experiments demonstrate the superior efficiency of the proposed method.

Condition number estimates for combined potential boundary integral operators in acoustic scattering

We study the classical combined field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle, namely the indirect formulation due to Brakhage-Werner/Leis/Panic, and the direct formulation associated with the names of Burton and Miller. We obtain lower and upper bounds on the condition numbers for these formulations, emphasising dependence on the frequency, the geometry of the scatterer, and the coupling parameter. Of independent interest we also obtain upper and lower bounds on the norms of two oscillatory integral operators, namely the classical acoustic single- and double-layer potential operators.

Pricing inefficiencies in private real estate markets using total return swaps

Efficient markets should guarantee the existence of zero spreads for total return swaps. However, real estate markets have recorded values that are significantly different from zero in both directions. Possible explanations might suggest non-rational behaviour by inexperienced market players or unusual features of the underlying asset market. We find that institutional characteristics in the underlying market lead to market inefficiencies and, hence, to the creation of a rational trading window with upper and lower bounds within which transactions do not offer arbitrage opportunities. Given the existence of this rational trading window, we also argue that the observed spreads can substantially be explained by trading imbalances due to the limited liquidity of a newly formed market and/or to the effect of market sentiment, complementing explanations based on the lag between underlying market returns and index returns.

Atmospheric predictability revisited

This article examines the potential to improve numerical weather prediction (NWP) by estimating upper and lower bounds on predictability by re-visiting the original study of Lorenz (1982) but applied to the most recent version of the European Centre for Medium Range Weather Forecasts (ECMWF) forecast system, for both the deterministic and ensemble prediction systems (EPS). These bounds are contrasted with an older version of the same NWP system to see how they have changed with improvements to the NWP system. The computations were performed for the earlier seasons of DJF 1985/1986 and JJA 1986 and the later seasons of DJF 2010/2011 and JJA 2011 using the 500-hPa geopotential height field. Results indicate that for this field, we may be approaching the limit of deterministic forecasting so that further improvements might only be obtained by improving the initial state. The results also show that predictability calculations with earlier versions of the model may overestimate potential forecast skill, which may be due to insufficient internal variability in the model and because recent versions of the model are more realistic in representing the true atmospheric evolution. The same methodology is applied to the EPS to calculate upper and lower bounds of predictability of the ensemble mean forecast in order to explore how ensemble forecasting could extend the limits of the deterministic forecast. The results show that there is a large potential to improve the ensemble predictions, but for the increased predictability of the ensemble mean, there will be a trade-off in information as the forecasts will become increasingly smoothed with time. From around the 10-d forecast time, the ensemble mean begins to converge towards climatology. Until this point, the ensemble mean is able to predict the main features of the large-scale flow accurately and with high consistency from one forecast cycle to the next. By the 15-d forecast time, the ensemble mean has lost information with the anomaly of the flow strongly smoothed out. In contrast, the control forecast is much less consistent from run to run, but provides more detailed (unsmoothed) but less useful information.

On the control of a non-ideal engineering system: A friction-driven oscillating system with limited power supply

In this work a switching feedback controller for stick-slip compensation of a 2-DOF mass-spring-belt system which interacts with an energy source of limited power supply (non-ideal case) is developed. The system presents an oscillatory behavior due to the stick-slip friction. As the system equilibrium for a conventional feedback controller is not the origin, a switching control law combining a state feedback term and a discontinuous term is proposed to regulate the position of the mass. The problem of tracking a desired periodic trajectory is also considered. The feedback system is robust with respect to the friction force that is assumed to be within known upper and lower bounds.

The non-adiabatic hyperspherical approach to the two-dimensional D- ion in the presence of a magnetic field

We have used the adiabatic hyperspherical approach to determine the energies and wave functions of the ground state and first excited states of a two-dimensional D- ion in the presence of a magnetic field. Using a modified hyperspherical angular variable, potential energy curves are analytically obtained, allowing an accurate determination of the energy levels of this system. Upper and lower bounds for the ground-state energy have been determined by a non-adiabatic procedure, as the purpose is to improve the accuracy of method. The results are shown to be comparable to the best variational calculations reported in the literature.

An equilibrium approach to modelling social interaction

The aim of this work is to put forward a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. After showing the formal equivalence linking econometric multinomial logit models to equilibrium statical mechanics, a multi- population generalization of the Curie-Weiss model for ferromagnets is considered as a starting point in developing a model capable of describing sudden shifts in aggregate human behaviour. Existence of the thermodynamic limit for the model is shown by an asymptotic sub-additivity method and factorization of correlation functions is proved almost everywhere. The exact solution for the model is provided in the thermodynamical limit by nding converging upper and lower bounds for the system's pressure, and the solution is used to prove an analytic result regarding the number of possible equilibrium states of a two-population system. The work stresses the importance of linking regimes predicted by the model to real phenomena, and to this end it proposes two possible procedures to estimate the model's parameters starting from micro-level data. These are applied to three case studies based on census type data: though these studies are found to be ultimately inconclusive on an empirical level, considerations are drawn that encourage further refinements of the chosen modelling approach, to be considered in future work.